Question

Marks	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40	40-45	45-50
Frequency	3	5	7	8	10	11	14	19	15	13

For the following distribution, find the mean using step deviation method. (Round off your answer to the nearest whole number)

• A. $29$
• B. $31$
• C. $35$
• D. $37$

Answer 1

Answer: (B)

$31$

X	Mid point (x)	Frequency (F)	i=class interval width	A=22.5 Assumed mean	u=$\frac{x-A}{i}$	fu
0-5	2.5	3	5	22.5	-4	-12
5-10	7.5	5	5	22.5	-3	-15
10 -15	12.5	7	5	22.5	-2	-14
15-20	17.5	8	5	22.5	-1	-8
20-25	22.5=A	10	5	22.5	0	0
25-30	27.5	11	5	22.5	1	11
30-35	32.5	14	5	22.5	2	28
35-40	37.5	19	5	22. 5	3	57
40-45	42.5	15	5	22.5	4	60
45-50	47.5	13	5	22.5	5	65
		$\Sigma f=105$				$\Sigma fu=172$

The formula used for arithmetic mean of grouped data by step deviation method is, $\overline{X}=A+\frac{\sum fu}{\sum f}\times i$
$A=$ Assumed mean of the given data
$\sum$ = Summation of the frequencies given in the grouped data
$\sum fu$ = Summation of the frequencies and deviation of a given mean data
$u=\frac{(x-A)}{i}$
$i=$ Class interval width
$\overline{X}$ = arithmetic mean
$\overline{X}=22.5+\frac{172}{105}\times 5$
$=22.5+8.19$
$=30.69$ $\approx$ $31$